How do I push a crease in to make this mesh more "smooth?"
I suspect your topology might not be the best for this kind of object. Without suggesting mine is the best, or perfectly suits your purposes, here's a way of modelling it.


Starting with a half-cylinder, with loop-cuts as shown
Use the knife tool (K), cut a diagonal from the 2nd-bottom longitude to the 2nd-top longitude just inside the existing loops, and then extend the diagonal to the boundaries,  using the knife tool again, this time constraining it. (KC)
X Delete the inside faces, and ensuring the pivot is set on the center-line (see the last item) SY, scale the center section out appropriately
CtrlE, from the Edge Menu, 'Bridge Edge loops' having selected the loops on the sides of the gap.
CtrlR cut in some more holding loops .. (pressing E makes the new loop parallel to one side or the other, and pressing F flips which side)
Assign a Mirror modifier, and maybe a Subdivision modifier..


By using GG to slide edge-loops (with E and Fin the same way as when you made them,) you can tighten or loosen the creases between the sections by moving the holding loops in or out, or you can even get rid of the central loops. If you want to completely soften the creases, careful use of AltS to scale vertices out along their own normals, and CtrlV Vertex Menu > 'Smooth Vertex' will get you there, but that's destructive, so save snapshots.



This result may not be precisely what you want, but variations on this sort of approach may work for you



Here's a contrasting example, where the central loop in the crease has been removed, and its outside loops slid outwards, to soften the transition: